Abstract
We study the asymptotically flat quasi-local black hole/hairy black hole model with nonzero mass of the scalar field. We disclose effects of the scalar mass on transitions in a grand canonical ensemble with condensation behaviors of the parameter psi _{2}, which is similar to approaches in holographic theories. We find that a more negative scalar mass makes the phase transition easier. We also obtain the analytical relation psi _{2}varpropto (T_{c}-T)^{1/2} around the critical phase transition points, implying a second order phase transition. Besides the parameter psi _{2}, we show that metric solutions can be used to disclose properties of the transitions. In this work, we observe that phase transitions in a box are strikingly similar to holographic transitions in AdS gravity and the similarity provides insights into holographic theories.
Highlights
As is well known, the asymptotically flat Schwarzschild black holes usually have a negative specific heat and cannot be in equilibrium with the thermal radiation environment
We conclude that metric solutions can be used to disclose the threshold phase transition temperature and the order of transitions in asymptotically flat black hole/hairy black hole systems in a box, which is similar to the properties of holographic conductor/superconductor transitions in AdS gravity [67]
We studied a general four-dimensional black hole/hairy black hole transition model in a box with nonzero mass of the scalar field in a grand canonical ensemble
Summary
The asymptotically flat Schwarzschild black holes usually have a negative specific heat and cannot be in equilibrium with the thermal radiation environment. For a certain range of parameters, this model admits stable hairy black hole solutions, which provides a way to evade the flat space no-hair theorems Another important conclusion is that the overall phase structure of this gravity system in a box is strikingly similar to that of holographic superconductor systems in AdS gravity [43,44]. It is meaningful to generalize the quasi-local black hole/hairy black hole transition model in [42] by considering a nonzero mass of the scalar field since the mass usually plays a crucial role in determining the properties of transitions It was shown in holographic superconductor theories that a more negative mass corresponds to a larger holographic conductor/supercconductor phase transition temperature or a smaller mass makes the transition easier [46,47,48].
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